Geometric ZWEIER Convergent Lacunary Sequence Spaces

TL;DR

This paper introduces new lacunary strong geometric zweier convergent sequence spaces, explores their topological properties, and computes their lacunary statistical zweier convergence, expanding the framework of sequence space theory.

Contribution

It defines novel lacunary strong geometric zweier convergent sequence spaces and analyzes their topological and convergence properties.

Findings

Spaces are normed and topologically characterized.

Lacunary statistical zweier convergence is computed for these spaces.

Theoretical framework extends sequence space analysis with lacunary and geometric methods.

Abstract

The main purpose of this paper is to introduce lacunary strong geometric zweier convergent sequence spaces $N_{\theta }^{0} \left[Z\left(G\right)\right]$, $N_{\theta } \left[Z\left(G\right)\right]$, $N_{\theta }^{\infty } \left[Z\left(G\right)\right]$consisting of all sequences $x=\left(x_{k} \right)$such that $\left[Z\left(G\right)\right]x$ are in the spaces $N_{\theta }^{0} ,N_{\theta } {\rm and\; }N_{\theta }^{\infty } $ respectively, which are normed. We prove certain topological properties of these spaces and compute their lacunary stastical zweier convergence.